Is there a way to reduce the 'Power' and 'Size' of lights when scaling my scene down?
I don't think you can scale the lights with the regular "Scale" tool, but with a little script you can scale every light's energy and size using python. 

import bpy

factor = 2  # Replace this by your scale factor

for obj in bpy.data.lights:
    for attr in ('energy', 'shadow_soft_size', 'size'):
    # for attr in ('energy',):  # Replace if you only want to scale the energy
    # for attr in ('shadow_soft_size', 'size'):  # Replace if you only want to scale the size
        if hasattr(obj, attr):
            setattr(obj, attr, getattr(obj, attr) * factor)


Keep in mind that light energy decreases quadratically relatively to the distance it travels, so if you scale your scene by a factor of 2, you should increase the energy by a factor of 2^2 = 4. (Or 0.25 if you scale by a factor of 0.5)

Follow this if you don't know how to run a script in Blender.